Sunday, December 13, 2015

Acceleration of body on rough horizontal surface of accelerating Truck

Body on rough horizontal surface gets locked because of interlocking of irregular surfaces and it generates friction against the relative motion. If the body is on the rough surface of a truck that is accelerating, then the truck behaves like a non  inertial frame with respect to which we shall the study the motion by considering pseudo force. 

It is just because newton laws of motion are not valid in non inertial frame. To apply newton laws of motion to a body in non inertial frame, we shall apply virtual force on the body that is equal to the force on the system but in the opposite direction.

Thus a pseudo force comes into picture in this case. As this pseudo force acts in the back ward direction, the body is tend to move in the back ward direction and hence the frictional force is in the forward direction on the body against the relative motion.

If this pseudo force is less  than limiting frictional force, the block will be in the state of rest and static frictional force self adjusts itself the applied force.

If the truck starts moving with enough acceleration, the block also will have enough virtual force which can dominate the maximum static frictional force and hence the body  starts moving in the back ward direction.

We can measure the effective acceleration of the system using newton laws of motion. Force along the direction of motion shall be treated as positive and force against the motion shall be treated s negative.

Mathematical expression for this friction is derived in the following video lesson as shown below.

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